Greedy matching works as long as you're not using the /s modifier:

use strict;

my $string = join '', <DATA>;

if($string =~ /^Line3 : (.*)/m) {
    print "$1\n";
}

__DATA__
Line1 : Dit is de eerste regel
Line2 : Dit is de tweede regel
Line3 : Dit is de derde regel
Line4 : Dit is de vierde regel
[download]

The /m modifier is necessary to have the ^ anchor match the beginning of any line in a multi-line string. The greedy .* will then match anything until the end of that line.

Had you used the /s modifier, the greedy .* would have matched newlines as well and therefore gobbled up everything until the end of the multi-line string.

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